Let
be positive integers. Consider in a plane
two disjoint sets of points
and
consisting of
and
points, respectively, and such that no three points of the union
are collinear. Prove that there exists a straightline
with the following property: Each of the two half-planes determined by
on
(
not being included in either) contains exactly half of the points of
and exactly half of the points of
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Let $n_1, n_2$ be positive integers. Consider in a plane $E$ two disjoint sets of points $M_1$ and $M_2$ consisting of $2n_1$ and $2n_2$ points, respectively, and such that no three points of the union $M_1 \cup M_2$ are collinear. Prove that there exists a straightline $g$ with the following property: Each of the two half-planes determined by $g$ on $E$ ($g$ not being included in either) contains exactly half of the points of $M_1$ and exactly half of the points of $M_2.$